The no. plate of a bus had peculiarity. The bus number was a perfect square. It was also a perfect square when the plate was turned upside down. The bus company had only five hundred buses numbered from 1 to 500. What can be the number?

Since the bus has numbers from 1 to 500 and is a perfect square it has to be one of the numbers among

1 , 4 , 9 , ..... 484($$22^2$$)

When the plate is put upside down then also a number is obtained which is a perfect square.

It is possible when the digit on the plate contains only  digits 0,1,6,8 and 9

Among the options, 169 ($$13^2$$)is a perfect square which upon putting upside down gives 961($$31^2$$) which is also a perfect square